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The primary order parameter of hybrid improper ferroelectricity (HIF) is not spontaneous polarisation but nonpolar modes such as oxygen octahedral rotations (OORs), antipolar, or even Jahnâ€"Teller distortions; therefore, the HIF mechanism may be applied as an effective pathway to tune electronic bandgaps, control orbitals, and create multiferroicity. Most of the current experimental research on HIF is focused on layered perovskite oxides; therefore, this review focuses on the recent progress of experimental studies on HIF materials with the Ruddlesdenâ€"Popper (Râ€"P) and Dionâ€"Jacobson (Dâ€"J) structures. Experimental research on double-layered Râ€"P oxides is included, and the linear relationship between the Curie temperature and tolerance factor has been established. Moreover, the coexistence of polar and weak ferromagnetic phases has been observed in iron-based double-layered Râ€"P oxides at room temperature. The recent discovery of ferroelectricity in A-site cation-ordered triple-layered Râ€"P oxides has significantly expanded the HIF field. HIF has also been confirmed in caesium- and rubidium-based double-layered Dâ€"J oxides, and complex OOR modes have been observed in Dâ€"J oxides. Although significant progress has been achieved for HIF materials in layered perovskite oxides, extensive research is required to reveal the mysteries of HIF and to create single-phase multiferroics in HIF materials. [ABSTRACT FROM AUTHOR]